Wonders of Math

New -- 20 October 2005

This particular essay on the Wonders of Math came about in part by a reader pointing out that 9 divided by 9 is equal to 1... and not 0.999999999... The latter, of course, was a logical extension of the table previously provided in the treatise on nines and as duplicated here:

Number

Divided by 7

Divided by 9

1

0.142857 142857...

0.11111111111...

2

0.2857 142857 14...

0.22222222222...

3

0.42857 142857 1...

0.33333333333...

4

0.57 142857 1428...

0.44444444444...

5

0.7 142857 14285...

0.55555555555...

6

0.857 142857 142...

0.66666666666...

7

1.0000000000000...

0.77777777777...

8

1.142857 142857...

0.88888888888...

9

1.2857 142857 14...

0.99999999999... *

In the true spirit of creating our own reality and simultaneously demonstrating the fundamental interconnectedness of all things, events, and Seventh Calvary to the rescue type situations, four days later another reader [1] coincidentally provided the following argument for my enlightenment -- and also for my use against naysayers, however appropriate such naysaying may have been. [This revelationary exposition of the Wonders of Math was, by the way, apparently learned from his 9th grade teacher, a Mr. Schultz -- 9th grade! -- proving, incidentally, that Fred was listening in class after all!]

The precise mathematical proof consists of assuming first a number N which is defined by:

N = 0.999999999...

If we now multiply both sides of the equation by 10, we obtain:

10N = 9.999999999...

Now substracting N from each side of the equation, we obtain:

10N - N = 9.999999999... - N = 9.999999999... - 0.999999999... = 9

I.e.

9N = 9

or

N = 1 = 0.999999999...

Q. E. D., Thus it is conclusively proved.

Isn't mathematics just wonderful!?

**************

For the mathematically inclined... yes, if one goes to the end of the sequences of 9s in the numbers for 10N and N, one sequence will have a zero and one will have a 9. But this end is at infinity, i.e. undefined. Furthermore, are we really going to argue about 1 part in ten to the gazillion quadrillion decimal places?